Respuesta :
[tex]\bf recall\\\\
log_{{ a}}{{ b}}=y \iff {{ a}}^y={{ b}}\qquad\qquad
{{ a}}^y={{ b}}\iff log_{{ a}}{{ b}}=y \\\\
-----------------------------\\\\
thus\qquad
\begin{array}{cc|llll}
x&y&5^y=x\\
\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\
25&2&5^2=25\\
125&3&5^3=125\\
625&4&5^4=625\\
\end{array}
\\\\\\
\textit{so hmmm what would that be in log notation? }\ 5^y=x \iff \boxed{?}[/tex]
Answer:
[tex]f(x) =log_5 x[/tex]
Step-by-step explanation:
Here f(x) =2 when x = 25 that is [tex]5^{2}[/tex]
f(x) = 3 when x = 125 that is [tex]5^{3}[/tex]
f(x) = 4 when x =625 that is [tex]5^{4}[/tex]
[tex]f(x) =log_5 x[/tex]
here we can see that each value is exponent of 5
therefore function must be log function with base 5
so it is [tex]f(x) =log_5 x[/tex]
